Math Problem Statement

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Find the function value for V(r) = (4/3)πr^3. Solve for (a) V(2), (b) V(√(3/2)), (c) V(3r).

Solution

Here are the results for the given function V(r)=43πr3V(r) = \frac{4}{3} \pi r^3:

(a) V(2)=10.67πV(2) = 10.67\pi

(b) V(32)=2.45πV\left(\sqrt{\frac{3}{2}}\right) = 2.45\pi

(c) V(3r)=36πr3V(3r) = 36\pi r^3

If you have any questions or need further details, feel free to ask!

Related Questions:

  1. How is the formula for the volume of a sphere derived?
  2. What happens to the volume when you triple the radius?
  3. How can you simplify the expression V(kr)V(kr) in general terms?
  4. What is the significance of π\pi in geometric problems like this?
  5. How can the volume formula be applied to real-world objects?

Tip: Always simplify expressions before substituting values to avoid errors in more complex calculations!

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Math Problem Analysis

Mathematical Concepts

Geometry
Algebra
Volume of a Sphere

Formulas

Volume of a sphere V(r) = (4/3)πr^3

Theorems

Formula for volume of a sphere

Suitable Grade Level

Grades 9-12